Clue
Handhold
noun
You learned that 掛かる can mean "to be hooked." If you're doing something physical like climbing and your hand hooks onto something, that thing is called a handhold.
Figuratively, this can also mean clue, since a clue is something you grasp onto, much like a handhold, to help you progress in solving a crime or mystery. This figurative use of 手掛かり is actually the most common!
The reading is 手 plus 掛かる put together. Just watch out for that rendaku.
手掛かりはまだ見つからないのですか。
Still can't find any clues?
今は全力で、問題解決の糸口となるような手掛かりを探しています。
We are currently searching wholeheartedly for clues that will lead us to a solution.
警察は消えたベーコンの謎について何か手掛かりを見つけましたか？
Have the police found any clues regarding the mystery of the vanishing bacon?
藤川さんの発言が、犯人のトリックを見抜く手掛かりになりました。
Mr. Fujikawa's statement provided a clue to the culprit's trickery.